Contents


Chapter 8

Equilibrium

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It is generally observed that many chemical reactions do not proceed to completion when they are carried out in a closed container. This implies that the reactants are not completely converted into products. Instead , after some time concentrations of the reactants do not undergo further decrease and the reaction appears to have stopped. This state of the system in which no further net change occurs is called a state of equilibrium. In all processes which attain equilibrium , two opposing forces are involved. Equilibrium is attained when rates of the two opposing processes become equal. If the opposing processes involve only physical changes, the equilibrium is called physical equilibrium. If the opposing processes are chemical reactions, the equilibrium is called chemical equilibrium. In spite of a large number and variety of chemical reactions, their state of chemical equilibrium may be classified in three groups characterized by the extent to which the reactions proceed.

  1. The reactions that proceed nearly to completion and only negligible concentration of the reactants is left.
  2. The reactions in which only small amounts of products are formed and most of the reactants remain unchanged at equilibrium stage.
  3. The reactions in which the concentrations of the reactants and products are comparable when the system is in equilibrium.

EQUILIBRIUM IN PHYSICAL PROCESSES

The equilibrium involving physical processes are referred to as physical equilibria. The physical equilibria involving change in state may be of the following three types.
                                        Solid Liquid
                                      Liquid Gas
                                       Solid Gas
SOLID-LIQUID EQUILIBRIUM

When a crystalline solid is heated , the temperature at which solid-liquid equilibrium is attained under 1 atmospheric pressure is called the normal melting point or normal freezing point of the substance. If heat energy is added to a mixture of solid and liquid at equilibrium, the solid is gradually converted into liquid while the temperature remains constant. If a solid-liquid system at melting point is taken in a well-insulated container, then this constitutes a system in which solid is in dynamic equilibrium with the liquid. For example, let us consider ice and water at 273 K (melting point of ice) , taken in a perfectly insulated thermos flask. It may be noted that, the temperature as well as the masses of ice and water remains constant. This represents a dynamic equilibrium between ice and water.
                                        ice water
                                H2O (s) H2O (l)
Since there is no change in mass of ice and water, the number of molecules going from ice into water is equal to the number of molecules of water going into ice.
Thus, at equilibrium,
                                    Rate of melting = Rate of freezing

LIQUID - VAPOUR EQUILIBRIUM

When a liquid is placed in an open container, it starts evaporating spontaneously. This is because a liquid is composed of molecules which are in constant rapid motion. The velocity distribution in a liquid is almost the same as in case of gases. All molecules of a liquid do not possess the same velocity. At all temperatures, a liquid possesses some molecules whose velocity and hence kinetic energy is much larger as compared to that of the rest of the molecules. When a molecule reaches the surface of the liquid , an inward pull due to surface tension acts on it. If the molecule possesses sufficient kinetic energy to overcome the inward pull due to surface tension, it comes out of the surface and collects over it (Fig a). Such molecules constitute the vapour and the process is called vapourisation or evaporation .

When a liquid is taken in a closed container having some free space over the liquid (Fig b), the energetic molecules collect in the free space due to vaporisation. Some of the vapour molecules however get condensed and return back to the liquid. The rate of condensation depends upon the concentration of molecules in the vapour phase. The rate of evaporation remains constant throughout if the temperature is kept constant. Since the rate of condensation is proportional to the concentration of molecules in vapour phase, it slowly increases with time. After certain time, the rate of condensation becomes equal to rate of evaporation as shown graphically in Fig.

As soon as the rate of evaporation becomes equal to the rate of condensation, a state of dynamic equilibrium is attained which can be shown as follows:
                                                      LiquidVapour
It is to be noted that in a liquid vapour system, equilibrium can be attained only when the liquid is taken in a closed container. In an open container, vapour disperse in the atmosphere and equilibrium cannot be attained. In the state of equilibrium i.e., the state when the rate of evaporation and rate of condensation are exactly equal, a constant pressure of vapour is attained. The pressure at which the liquid and vapour phases exist together in equilibrium is called saturation vapour pressure or simply vapour pressure of the liquid at the same temperature. The liquid vapour equilibrium as described above is dynamic one. The two processes occur simultaneously in opposite direction but with equal rate i.e., at equilibrium.
                                                      Rate of evaporation = Rate of condensation
Liquid–vapour or liquid-gas equilibrium can be illustrated by taking a small amount of water at room temperature in a evacuated vessel attached to a manometer as shown in Fig. Due to evaporation of water, a pressure is developed in the vessel and the mercury level in the manometer rises gradually. After some time , the mercury level in the manometer becomes steady (Fig b) . This indicates that no more water is evaporating although liquid water is still present in the vessel. This shows that a state of equilibrium has been attained as shown below :
                                                      H2O( l ) H2O(g)
At this stage , the rate of evaporation of water molecules present in the liquid phase is equal to the rate of condensation of water molecules present in the gaseous phase (i.e., vapour phase).

SOLID – VAPOUR EQUILIBRIUM

Consider the systems where solids sublime to vapour phase. If we place solid iodine in a closed vessel, after some time the vessel gets filled up with violet vapour and the intensity of colour increases with time. After a certain time the intensity of colour becomes constant and at this stage equilibrium is attained. Hence solid iodine sublimes to give iodine vapour and the iodine vapour condenses to give solid iodine. The equilibrium can be represented as :
                                                      I2 (solid ) I2 (vapour)
Other examples showing this kind of equilibrium are :
                                          Camphor(solid ) Camphor (vapour)
                                               NH4Cl(solid ) NH4Cl (vapour)

EQUILIBRIUM INVOLVING DISSOLUTION OF SOLIDS OR GASES IN LIQUIDS

SOLIDS IN LIQUIDS

It is not possible to dissolve any amount of a solute in a given amount of solvent. For example, when we add sugar to water , the crystals of sugar keep on going into solution in the beginning. But after some time no more of sugar dissolves. A solution in which no more solute can be dissolved is called a saturated solution. The amount of solute required to prepare a saturated solution in a given quantity of solvent is known as solubility of the solute at a particular temperature.The saturated solution corresponds to the state of equilibrium. When we add sugar crystals to water, molecular vibration tends to dislodge molecules from the surface of crystals. The molecules of sugar which go into solution are free to move throughout the water. In the beginning, the rate at which molecules leave the crystal is much greater than the rate of their return. As the number of molecules in solution increases , the rate at which molecules return to crystal also increases. Soon a balance between the two rates i.e., the rate of dissolution and rate of precipitation is established and this corresponds to the state of equilibrium.
Thus, in a saturated solution, a dynamic equilibrium exists between the molecules of sugar in the solid state and the molecules of sugar in solution.
Sugar (in solution) Sugar(solid)
The dynamic nature of equilibrium can be demonstrated by adding radioactive sugar into a saturated solution of non-radioactive sugar (Fig).

It is observed that the solution and rest of the non-radioactive sugar also become radioactive. This shows that even at equilibrium, the process of dissolution and precipitation are taking place. This means that equilibrium is dynamic in nature. However, at equilibrium :
                                                      Rate of dissolution = Rate of precipitation.

GASES IN LIQUIDS

The gases can be dissolved in suitable liquids. At a given temperature, a liquid can dissolve only certain definite mass of the gas. This suggests that a state of equilibrium exists between molecules in the gaseous state and the molecules dissolved in the liquid. For example, when carbon dioxide is dissolved in soda water, the following equilibrium exists :
                                                      CO2(g) CO2(solution)
At equilibrium the rate at which gas molecule pass into the solution becomes equal to the rate at which dissolved gas molecules come back into the gaseous phase. This is shown in Fig.

The solubility of a gas in liquid depends on the pressure. The effect of pressure on the solubility of a gas in a liquid is given by Henry's law .

Henry's Law

The law can be stated as follows: The mass of a gas that dissolves in a given mass of a solvent at constant temperature is proportional to to the pressure of the gas at equilibrium with the solution provided the gas does not undergo any chemical change during the formation of a solution.
If the mass m of a gas dissolves in a given mass of a solvent at a particular temperature under the equilibrium pressure P , then according to Henry's Law, we have,
                                                      m α p
                                                      m = k p

where k is a proportionality constant.

Limitations of Henry's Law

Following are the limitations of Henry's law :

  1. Henry's law is applicable to ideal gases only. However, this law can be applied to real gases at low pressure when the real gases approach the behaviour of ideal gases.
  2. The law is not applicable to those gases which undergo a chemical change in solution. For example, the law cannot be applied to ammonia which reacts with water to form NH4OH.
  3. The law cannot be applied to those gases which dissociate into ions in solution. For example, the law cannot be applied to HCl gas because it dissociates into H+ and Cl ions in solution.
    A soda water bottle contains CO2gas dissolved in water at a higher pressure and posses the following equilibria:
                                                CO2(g) CO2 (solution)
    Since the soda water bottle is sealed when the gas is at high pressure, there is quite appreciable amount of carbon dioxide dissolved in water and the gas pressure above the solution is high. When the bottle is opened, the pressure of the gas above the solution decreases, therefore, the dissolved gas escapes (fizzes out) to attain new equilibrium state.
    The solubility of a gas in a liquid decreases with increase in temperature.

GENERAL CHARACTERISTICS OF EQUILIBRIA INVOLVING PHYSICAL PROCESSES

From the discussions of physical equilibria, the following points are noted :

  1. In the case of Liquid vapour equilibrium, the vapour pressure is a constant at a given temperature.
  2. For solid Liquid equilibrium , there is only one temperature(melting point) at 1 atm at which the two phases can coexist without any exchange of heat with the surroundings, the mass of the two phases remain constant.
  3. For dissolution of solids in liquids, the solubility is constant at a given temperature.
  4. For dissolution of gases in liquids the concentration of a gas in liquid is proportional to the pressure(concentration) of the gas over the liquid.

These four concentration-related findings are expressed in the TABLE below:

Some Features of Physical Equilibria

Process

Conclusions

H2O( l ) H2 O(g)

PH2O is constant at given temperature.

H2O(s) H2O( l )

Melting point is fixed at constant pressure

Solute(s) Solute(solution)

Concentration of solute in solution is constant at a given temperature.

Gas Solution
CO2(g)CO2(aq)

[gas(aq)] / [gas(g)] is constant at a given temperature.
[CO2(aq) ]/ [CO2(g)] is constant at a given temperature.

General Characteristics of Equilibria Involving Physical Processes

From the physical equilibria discussed above the characteristics of the systems may be stated as follows:

  1. The system has to be closed; that it should not gain matter from the surroundings nor lose matter to the surroundings.
  2. There is a dynamic but stable condition. Two opposite processes occur at the same rate.
  3. The measurable properties of the system remain constant, since the concentration of the substances remain constant.
  4. When equilibrium is attained, there exists an expression involving concentration of reacting substances which reaches a constant value at a given temperature. The TABLE above lists the concentration-related expressions for certain physical processes.
  5. The magnitude of the constant value of the concentration-related expressions is an indication of the extent to which the reaction proceeds before reaching equilibrium.

 

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